Perfect Competition

Review

Hans Martinez

Western University

Perfect Competition (Review)

  • What is Perfect Competition?
  • Profit Maximization by a Price-Taking Firm
  • Functional Forms
  • Revealed Profitability
  • Supply Curve of a Firm

Perfectly Competitive Markets

  • A perfectly competitive market consists of firms that produce identical products that sell at the same price

  • Each firm’s volume of output is so small in comparison to the overall market demand that no single firm has an impact on the market price

Perfectly Competitive Markets - Conditions

  1. The industry is fragmented
    • It consists of many buyers and sellers
  2. Firms produce undifferentiated products
    • Consumers perceive the products to be identical no matter who produces them

Perfectly Competitive Markets - Conditions

  1. Consumers have perfect information about prices
    • The industry is characterized by equal access to resources
  2. All firms —incumbents and prospective entrants— have access to the same technology and inputs

Implications of Conditions

  • The first characteristic implies that sellers and buyers act as price-takers

  • The second and third characteristics imply a law of one price

  • The fourth characteristic implies that the industry is characterized by free entry

The Profit Maximization Hypothesis

\[ \begin{align} \max_{Q} \pi(Q)&=TR(Q)-TC(Q) \\ \text{s.t. } Q&\ge0 \end{align} \qquad(1)\]

  • Economic Profit = Sales Revenue - Economic (Opportunity) Cost

  • firm sells output Q; TR(Q), revenue from selling the quantity; TC(Q), economic cost of producing the quantity Q

The Profit Maximization Condition Continued

  • The profit maximization condition is

\[ \frac{dTR(Q)}{dQ}= \frac{dTC(Q)}{dQ} \]

  • Marginal revenue equals marginal cost

Functional Forms

  • We can define our problem in several ways depending on the question we’re interested in
  1. Output quantities: \(TR(Q)=PQ\) and \(TC(Q)\)

  2. Input quantities: \(TR(K,L)=Pf(K,L)\) and \(TC(K,L)=rK+wL\)

Graphs

Conditions for an interior optimum

  • \(\frac{dTC(Q)}{Q}\) should be increasing

  • \(\frac{df(\bar K,L)}{dL}\) should be decreasing

Revealed Profitability

Supply Curve of a firm

  • The firm’s (short-run) supply function is defined by:
  1. P=SMC, where SMC slopes upward as long as P > Ps

  2. 0 where P < Ps

Review Questions

  • Productivity

  • Carbon tax